Risk-Averse Design Optimization via Tail-Region Correction of a Multi-fidelity DD-GPCE Surrogate Model

  • Lee, Gyeolhee (Hanyang University)
  • Lee, Dongjin (Hanyang University)

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Risk-averse design optimization constraints risk measures, such as the conditional value-at-risk (CVaR), to explicitly control extreme event behaivor in an engineering system. However, conventional risk-based design optimization is often limited by surrogate bias and sample scarcity in the tail region of the response distribution, particularly when estimating CVaR and other risk measures under high-dimensional and correlated uncertainties [1]. This study presents a risk-averse design optimization framework that uses a multi-fidelity, dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) surrogate model enhanced by a novel tail-region correction strategy. The proposed method constructs a confidence interval-based ϵ-risk region using the prediction variance of the DD-GPCE surrogate and selectively incorporates a small number of high-fidelity evaluations to locally correct surrogate predictions in the tail region. This correction significantly improves the accuracy and stability of CVaR estimation while minimizing the number of expensive simulations. A truss design problem demonstrates the accuracy and efficiency of the proposed method. The results show that the tail-corrected DD-GPCE model reduces tail-region prediction errors by 95.8% compared to the original DD-GPCE model and more reliably satisfies the CVaR-based design constraints. The overall computational cost of the optimization is reduced by a factor of 26.6 relative to the existing importance sampling-based multi-fidelity approach [2], highlighting the practicality of the proposed method for engineering design problems characterized by nonlinear responses and high-dimensional inputs.